Approximability of the capacitated b-edge dominating set problem

Authors:
André Berger;Takuro Fukunaga;Hiroshi Nagamochi;Ojas Parekh
Affiliations:
Department of Mathematics, Technical University Berlin, 10623, Germany;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

In this paper, we discuss the approximability of the capacitated b-edge dominating set problem, which generalizes the edge dominating set problem by introducing capacities and demands on the edges. We present an approximation algorithm for this problem and show that it achieves a factor of 8/3 for general graphs and a factor of 2 for bipartite graphs. Moreover, we discuss the relationships of the edge dominating set problem and the vertex cover problem. The results show that improving the approximation factor beyond 8/3 using our approach of adding valid inequalities to a natural linear programming relaxation is as hard as improving the approximation factor for vertex cover beyond 2.